1. Field of the Invention
The invention relates to a method of obtaining a 2D or 3D model if representative of a heterogeneous medium such as the subsoil, described by physical parameters or quantities, from data obtained by indirect measurements obtained from outside the medium, and other data, notably a set of isolated data measured in situ, all these data forming the a priori known information on the medium.
2. Description of the Prior Art
In the case of a medium such as the subsoil, the descriptive physical parameters are for example the impedance thereof in relation to P waves or S waves, or the density thereof. The direct and indirect data available are for example logs, seismic exploration data, and other data obtained from previous geologic surveys of the medium.
The waves emitted in the medium by a seismic source are propagated in the subsoil and are reflected on the discontinuities of the medium. They are recorded by pickups coupled with the underground formation and collected by an acquisition device.
Inversion methods have been developed, which connect a physical quantity of a heterogeneous medium such as the impedance thereof in relation to elastic waves to seismic data, to data measured in situ and to observations or interpretations.
A starting point is defining an a priori (1D, 2D or 3D) model of one or more physical parameters of the medium constructed by interpretation of known data, and covariance operators describing uncertainties about the a priori model and uncertainties about the known data. Synthetic seismograms, which constitute the response of the model, are constructed. The synthetic seismograms are compared with the real seismograms obtained by seismic exploration and the differences observed are gradually minimized according to norms associated with covariance operators selected according to an evaluation of the uncertainties about the a priori model and the seismic records.
The various known approaches differ notably in the number of physical parameters describing the medium, the dimension of the a priori model and the vast amount of possibilities offered when taking account of the uncertainty parameters. The known approaches obtain the optimum model minimizing an objective function, the sum of an objective function referred to as seismic and of an objective function referred to as geologic.
The seismic objective function represents the difference (in the sense of the norm induced by the covariance operator relative to the data) between the observed data and the synthetic data. The synthetic data are obtained by accounting for a complex propagation model.
The geologic objective function measures the difference in relation to the a priori model (in the sense of the norm induced by the covariance operator relative to the medium).
An example of one of these methods is described by Brac J. et al;  less than  less than Inversion with A Priori Information: an Approach to Integrated Stratigraphic Interpretation greater than  greater than ; in Sheriff R. E. Ed., Reservoir Geophysics, Soc. Expl. Geophys., Investigations in Geophysics 7.
Another method of 2D modeling of a physical quantity by stratigraphic inversion is also described in U.S. Pat. No. 4,972,383 filed by assignee.
French Patent No. 2,765,692 filed by the assignee describes a method of the same type intended for 3D modeling of a physical parameter or quantity such as the impedance of a heterogeneous medium, with construction of an a priori model from a 3D geometric model comprising several foliated volumes (sedimentary units) and also from known values of the quantity at several points of the medium, selection of a covariance model along the sheets of the various volumes and formation of an optimum model by means of an inversion process from the a priori model.
The previous methods model only the variation of a single physical parameter in the medium considered. Furthermore, the parameters used to describe the uncertainties about the a priori model (parameters defining the covariance operator) are constant throughout the domain or per geologic unit.
There are methods allowing modeling several physical quantities or parameters in a medium. They are notably described by:
Simmons and Backus, 1996:  less than  less than Waveform-based inversion and AVO prediction-error greater than  greater than , in Geophysics, 61, p. 1575-1588, or by Pan et al., 1994:  less than  less than An Integrated Target Oriented Prestack Elastic Waveform Inversion: Sensitivity, Calibration and Application)), in Geophysics, 59, 9, p. 1392-1404.
However, the a priori models considered within the scope of these known methods are of 1D type (they only depend on the depth), and each group of traces relative to a given lateral position of the medium (CDP) is processed independently from one lateral position to another.
The method according to the invention extends the approach developed in the two patents mentioned above to the case of several physical quantities or parameters while making possible variation, at any point of the medium, the uncertainty parameters describing the uncertainties about the a priori model, under certain conditions.
The method according to the invention finds applications in various fields, according to the type of waves (elastic waves, electromagnetic waves, etc.) emitted in order to obtain indirect measurements of a medium.
The seismic data used within the scope of the present method may contain information on the amplitude variation with the offset: prestack data, data linked with the technique known to the man skilled in the art referred to as intercept-gradient technique, extracted from the analysis of the variation, etc., or they may not contain them: poststack data.
The method of the invention is notably used with oil exploration in order to obtain quantitative representations and finer images of the structure or configuration of an underground zone, and facilitates identification of hydrocarbon reservoirs.
The objective of the method is to determine an optimum 2 or 3 dimensional (2D or 3D) model representative of the variation, in a heterogeneous medium, of several physical parameters from known data obtained by various methods: recorded data corresponding to waves reflected by the discontinuities of the medium in response to waves propagated therein, and from an a priori (2D or 3D) model of the heterogeneous medium, while taking account of the uncertainties about the recorded data and the a priori model.
The method according to the invention obtains an optimized 2D or 3D model representative of a heterogeneous medium such as the subsoil, described by at least one or more physical parameters or quantities, from recorded data corresponding to waves reflected by the medium and picked up by receivers coupled with the medium, in response to waves transmitted therein by a source, and from a priori information including data measured in situ.
The method comprises constructing a 2D or 3D geometric model describing correlation lines or surfaces, constructing a 2D or 3D a priori model described by one or more physical parameters, from the geometric model and data measured in situ for the physical parameters, at various points of the heterogeneous medium, and forming an optimum model by inversion of the recorded data by taking into account all the a priori information.
With the invention an operator for modeling the uncertainties about the a priori model is selected, which accounts for a degree of confidence for the a priori model variable at any point.
An exponential covariance model is for example selected, which can be variable according to the location in the medium. The covariance model selected may be a 1D model, a 1D model along the correlation lines, A 2D model, a 2D model along the correlation surfaces or a 3D model.
According to one or more embodiments, the exponential covariance model is relative to several parameters.
The model is described by several physical parameters, the covariance operator is for example modified so as to define differences in relation to the a priori model for other physical parameters, so that these differences are independent at each given point of the medium. The covariance model is for example anisotropic, with different correlation lengths in different directions in the medium.
According to an embodiment, formation of the optimum model with several physical parameters is obtained by minimizing a global objective function comprising a term relative to the recorded data, proportional to the square of the norm L2 of the difference between synthetic data and the recorded data, and a term relative to the medium consisting, in the case of a 2D (respectively 3D) model, on the one hand of the square of the norm L2 of the difference in relation to the a priori model expressed by the other physical parameters and, on the other hand, of the square of the norm L2 of the gradient of the difference, projected from the gradient onto the tangent to the local correlation line (respectively onto the plane tangent to the local correlation surface).
In the case of a 3D a priori model, the term relative to the medium can be formed from the square of the norm L2 of the difference in relation to the a priori model measured in relation to the other physical parameters, from the norm L2 of the gradient of the difference, and from the square of the Laplacian operator of the difference.
The method according to the invention can be applied for modeling a zone of the subsoil, with in situ measurements being obtained at various depths in one or more wells through the zone, the waves emitted being elastic waves.
The method according to the invention can also be applied for modeling a zone of a medium where the waves emitted are electromagnetic waves.
The invention does:
on the one hand, estimate several physical parameters describing the heterogeneous medium, which consequently allows better characterization of the medium, and
on the other hand, accounts for very rich a priori information concerning the dimension of the a priori model as well as the uncertainties relative thereto.